Question

Arthur Meiners is the production manager for Wheel-Rite, a small manufacturer of metal parts. Wheel-Rite sells 10,378 gear wheels each year. Wheel-Rite setup cost is $45 and maintenance cost is $0.60 per sprocket per year. Wheel-Rite can produce 493 gear wheels per day. The daily demand for the gear wheels is 51 units. Show your work.

1. What inventory management model should we use to solve this problem?
Model for discount purchases
Model Economic Quantity to Order
Model Economic Quantity to Produce
Model to handle dependent demand
2. What is the optimal amount of production? 3. What is the maximum inventory level of gear wheels that will be in the Wheel-Rite warehouse? 4. What is Wheel-Rite's annual setup cost? 5. What is the annual cost of maintaining Wheel-Rite?

Answer 1

1. The appropriate inventory management model to solve this problem is the Economic Quantity to Produce (EOQ) model. The EOQ model is used to determine the optimal order quantity or production quantity that minimizes the total cost of inventory, taking into account three cost types: setup, production, and holding.

2. To calculate the optimal amount of production using the EOQ model, we need the following information:
- Demand per year (D) = 10,378 gear wheels
- Setup cost (S)= $45
- Production rate per day (P) = 493 gear wheels
- Working days per year (W) = 365 (assuming no downtime)

The formula to calculate the EOQ is:

EOQ = sqrt((2 * D * S) / (P * (1 - (D / (P * W)))))

Plugging in the values:

EOQ = sqrt((2 * 10,378 * 45) / (493 * (1 - (10,378 / (493 * 365)))))

Calculating this equation will give you the optimal amount of production.

3. The maximum inventory level of gear wheels that will be in the Wheel-Rite warehouse can be calculated by multiplying the optimal amount of production (EOQ) by the number of production cycles in a year. The number of production cycles can be calculated by dividing the annual demand (D) by the optimal amount of production (EOQ) and rounding up to the nearest whole number.

Maximum inventory level = EOQ * ceil(D / EOQ)

4. Wheel-Rite's annual setup cost can be calculated by multiplying the setup cost (S) by the number of production cycles in a year.

Annual setup cost = S * ceil(D / EOQ)

5. Wheel-Rite's annual cost of maintaining inventory can be calculated by multiplying the holding cost per unit (which is the maintenance cost per sprocket per year) by the average inventory level. The average inventory level can be calculated by dividing the maximum inventory level by 2.

Annual cost of maintaining inventory = (Holding cost per unit) * (Average inventory level)

In this case, the holding cost per unit is $0.60 per sprocket per year, and the average inventory level can be calculated as (Maximum inventory level / 2).

Please note that you need the calculated EOQ value from question 2 to answer questions 3, 4, and 5.8